Homework 3

  • Due Mar 11, 2020 by 11:59pm
  • Points 100
  • Submitting a file upload

Problem 4. Evaluate the quantity γmB/kBT and the Larmor frequency for electron spins and proton spins in magnetic fields of 0.5 and 4.0 T at body temperature (310 K).

Problem 14. Use Eqs. 18.32 to find the magnetic field at one proton due to the other proton in a water molecule when both proton spins are parallel to each other and perpendicular to the line between the protons. The two protons form an angle of 104.5◦ and are each 96.5 × 10−12 m from the oxygen. Hint:  μz = γ Sz = γ h(bar)/2

Problem 15. The magnetic field at a distance of 0.15 nm from a proton is 4 × 10−4 T. What change in Larmor frequency does this ΔB cause? How long will it take for a phase difference of π radians to occur between a precessing spin feeling this extra field and one that is not?

Problem 20. Redraw the plot in Fig. 18.12, assuming protons and your static magnetic field is either 1.5 or 4 T. Explain how T1 and T2 depend on the magnetic field. Hint: For the plots use the following correlation times: 10-12, 10-11, 10-10, 10-9, 10-8, 10-7, 10-6, 10-5, and 10-4

Problem 23. Consider increasing B0 from 4 T to 7 T. Discuss what changes this will make in:

(a) the frequency of the RF pulse

(b) the signal recorded by the detection coil

(c) the values of T1 and T2

 

1583985599 03/11/2020 11:59pm